First, take the square root of each side of the equation to solve for #k# while keeping the equation balanced. Remember, the square root of a number produces both a positive and negative result.
#sqrt(k^2) = +-sqrt(76)#
#k = +-sqrt(76)#
We can now simplify this using this rule for radicals:
#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#
#k = +-sqrt(color(red)(4) xx color(blue)(19))#
#k = +-sqrt(color(red)(4)) xx sqrt(color(blue)(19))#
#k = +-2 xx sqrt(color(blue)(19))#
#k = +-2sqrt(color(blue)(19))#
If necessary: #sqrt(19) = 4.359# rounded to the nearest thousandth
#k = +-2 * 4.359#
#k = +-8.718# rounded to the nearest thousandth
